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2 years ago

Which interval contains a local minimum for the grafted function? [-4, -2.5] [-2, -1] [1, 2] [2.5, 4]

Mathematics

1 answer:

olga_2 [115]2 years ago

7 0

Answer:

Last option [2.5, 4]

Step-by-step explanation:

The local minima of a function are the points where the slope of the curve is zero and the function reaches a minimum value.

If, on the contrary, the function reaches a maximum value, then that point is a local maximum.

Observe, for example, the point (3, -4). Note that a line tangent to that point would be horizontal, that is, of slope m = 0. This point is a minimum of the function, because there are no values x to the right x = 3 or to the left of x = 3 for which $f(x)$

Now we must search among the options that interval contains at this point.

The intervals [-4, -2.5] [-2, -1] do not contain any local minimum

The intervalor [1, 2] contains a local maximum.

The only interval that contains a local minimum is [2.5, 4], which contains the point (3, -4)

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Solve the system of equations algebraically. Verify your

xz_007 [3.2K]

Answer:

The solution is the point (0.5,-3)

Step-by-step explanation:

we have

$y=4x-5$ ----> equation A

$y=-3$ ----> equation B

Solve the system by substitution

Substitute equation B in equation A

$-3=4x-5$

Solve for x

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$-3+5=4x$

$2=4x$

Divide by 4 both sides

$x=0.5$

therefore

The solution is the point (0.5,-3)

<em>Verify your answer using the graph</em>

using a graphing tool

Remember that the solution of the system of equations is the intersection point both graphs

The intersection point is (0.5,-3)

therefore

The solution is the point (0.5,-3)

see the attached figure

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2 years ago

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Question:

a. A = (2πr)(r)

b. A = (2πr)(2r)

c. $A =\frac{1}{2} (2\pi r)(r)$

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Answer:

The correct option is $A =\frac{1}{2} (2\pi r)(r)$

Step-by-step explanation:

The formula for the area, A of a parallelogram = base, b × height, h

Therefore, since the base dimension is approximately half the perimeter of a circle, we have;

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